We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG, and SIPG schemes. The derived schemes possess combined advantages of EulerianLagrangian methods and discontinuous Galerkin methods. An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm ...

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...

Abstract. In this paper, we investigate the superconvergence properties and a posteriori error estimates of a local discontinuous Galerkin (LDG) method for solving the one-dimensional linear fourth-order initial-boundary value problems arising in study of transverse vibrations of beams. We present a local error analysis to show that the leading terms of the local spatial discretization errors f...

Stokes flows are a type of fluid flow where convective forces small in comparison with viscous forces, and momentum transport is entirely due to diffusion. Besides being routinely used as benchmark test cases numerical dynamics, relevant several applications science engineering including porous media flow, biological flows, microfluidics, microrobotics, hydrodynamic lubrication. The present stu...

A novel strategy for the Hybridizable Discontinuous Galerkin (HDG) solution of heat bimaterial problems is proposed. It is based on eXtended Finite Element philosophy, together with a level set description of interfaces. Heaviside enrichment on cut elements and cut faces is used to represent discontinuities across the interface. A suitable weak form for the HDG local problem on cut elements is ...

We provide a projection-based analysis of a large class of finite element methods for second order elliptic problems. It includes the hybridized version of the main mixed and hybridizable discontinuous Galerkin methods. The main feature of this unifying approach is that it reduces the main difficulty of the analysis to the verification of some properties of an auxiliary, locally defined project...

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter all...

In this paper, a nonconforming mixed finite element approximating to the three-dimensional time-harmonic Maxwell’s equations is presented. On a uniform rectangular prism mesh, superclose property is achieved for electric field E and magnetic field H with the boundary condition E × n = 0 by means of the asymptotic expansion. Applying postprocessing operators, a superconvergence result is stated ...